Mathematical Sciences: Numerical Assessments of Goodness-of Fit Tests based on Statistically Equivalent Blocks

这项研究将检查拟合优度测试， 使用无分布或 非参数模型 小样本检验行为 基于间距的统计数据将使用Monte Carlo方法，并将其与极限分布进行比较 理论结果。 通过构造统计上等价的 块，检验统计量可以扩展到多维 案子 当试图代表一个潜在的解释或 描述模型的真实的多元数据，一个关键的 困难的是确定假设的模型何时是适当的。 最初的数学假设越少， 一般来说，很难确定模型确实代表了 重要的特征，但不是特定样本的任何伪像。 一些数学理论已经发展的情况下， 任意大的样本;一些理论已经开发时， 假设数据遵循高斯（正态）分布。 这 项目将检查测试模型的充分性时，样本是 不是非常大，同时分布也不能 被认为是正常的。 这项工作将集中在多方面- 变量观测

This research will examine goodness-of-fit tests for multivariate data modeled using distribution-free or nonparametric models. The small sample behavior of test statistics based on spacings will be investigated using Monte Carlo methods and will be compared to limiting distribution theoretical results. By constructing statistically equivalent blocks, test statistics can be extended to the multidimensional case. When trying to represent an underlying explanatory or descriptive model for real multivariate data, a crucial difficulty is to determine when a postulated model is adequate. The fewer the mathematical assumptions made initially, the more difficult in general to be sure that the model does represent the important features, but not any artifacts of a particular sample. Some mathematical theory has been developed for the case of an arbitrarily large sample; some theory has been developed when the data is assumed to follow a Gaussian (normal) distribution. This project will examine tests of model adequacy when the samples are not extremely large and at the same time the distribution cannot be assumed to be normal. The work will concentrate on multi- variate observations.